Minimal Partial Languages and Automata

  • Francine Blanchet-Sadri
  • Kira Goldner
  • Aidan Shackleton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8587)


Partial words are sequences of characters from an alphabet in which some positions may be marked with a “hole” symbol, ⋄. We can create a ⋄-substitution mapping this symbol to a subset of the alphabet, so that applying such a substitution to a partial word results in a set of full words (ones without holes). This setup allows us to compress regular languages into smaller partial languages. Deterministic finite automata for such partial languages, referred to as ⋄-DFAs, employ a limited non-determinism that can allow them to have lower state complexity than the minimal DFAs for the corresponding full languages. Our paper focuses on algorithms for the construction of minimal partial languages, associated with some ⋄-substitution, as well as approximation algorithms for the construction of minimal ⋄-DFAs.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Kira Goldner
    • 2
  • Aidan Shackleton
    • 3
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsOberlin CollegeOberlinUSA
  3. 3.Department of Computer ScienceSwarthmore CollegeSwarthmoreUSA

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